Logic of prototypes and counterexamples: possibilities and limits

Abstract

Fuzzy sets are a popular tool to model vague properties. It is, however, well-known that this model usually involves a good degree of arbitrariness. In this contribution we consider the possibility of standardising the construction of fuzzy sets at least with regard to the borderline cases. To this end, we identify a vague property with the sets of clearly positive cases and clearly negative cases and under the assumption that the universe of discourse is a metric space, we determine the fuzzy set by what can be described as a linear interpolation. Following this idea, we discuss a number of logic-based approaches to reasoning under vagueness.